# Oscillation tests for linear difference equations with non-monotone arguments

In: Tatra Mountains Mathematical Publications, vol. 79, no. 2
George E. Chatzarakis - Said R. Grace - Irena Jadlovská

## Details:

Year, pages: 2021, 81 - 100
Language: eng
Keywords:
non-monotone argument, retarded argument, advanced argument, oscillation, Gr\"{o}nwall inequality
Article type: Mathematics
Document type: scientific paper
This paper presents sufficient conditions involving $\lim \sup$ for the oscillation of all solutions of linear difference equations with general deviating argument of the form \begin{equation*} Δ x(n)+p(n)x(τ (n))=0, n\in\mathbb{N}0 [ \nabla x(n)-q(n)x(σ (n))=0, n\in \mathbb{N} ], \end{equation*} where \begin{align*} (p(n))n≥ 0 and (q(n))n≥ 1 are sequences of nonnegative real numbers and (τ (n))n≥ 0, (σ (n))n≥ 1 \end{align*} are (not necessarily monotone) sequences of integers. The results obtained improve all well-known results existing in the literature and an example, numerically solved in MATLAB, illustrating the significance of these results is provided.